Accuracy of visual interpolation between circular scale markers as a function of the separation between markers.

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Abstract
The accuracy of visual interpolation between the circular scale markers of a polar coordinate plot was studied as a function of the size of the scale interval. The interval sizes studied were 0.125, 0.5, 1, 2, 4, 5, 6, 8, and 10 inches. The 1st 7 of these scales were studied on a 10-inch diam. display while the latter 7 (including duplications of the 1, 2, 4, and 5 inch scales) were tested on a display 20 inches in diam. The principal finding of this study was that the errors of interpolation (expressed as proportions of the intervals in which the estimations are made) are large for scale intervals 0.125 inch in size (18%), and decrease rapidly as the scale interval increases in size up to 0.5 inch (4%). Increases in the size of the scale interval beyond 0.5 inch do not further reduce errors of estimation. Expressed as absolute errors of estimation in mm., the errors of localization are constant for the 3 smallest scale intervals tested(0.125, 0.25, and 0.5 inch) and increase linearly thereafter for larger scale units. For the larger scale units the Weber fraction was a constant. Individuals differ significantly in their ability to perform this kind of visual interpolation.

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